Block #149,460

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/4/2013, 9:27:52 AM · Difficulty 9.8573 · 6,640,267 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
f66185d2224ca188cd9fe69b7ecde227e548f67330127575fb3264f52dc01981

Height

#149,460

Difficulty

9.857295

Transactions

2

Size

472 B

Version

2

Bits

09db77b1

Nonce

63,123

Timestamp

9/4/2013, 9:27:52 AM

Confirmations

6,640,267

Merkle Root

9be0b2a1dc9c3003baecf2d84ac2ecb963b54b783dd8101418cae1bc84ff9be5
Transactions (2)
1 in → 1 out10.2900 XPM109 B
2 in → 1 out20.6100 XPM273 B
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.803 × 10⁹⁵(96-digit number)
48037072498965571285…27303746987526918721
Discovered Prime Numbers
p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
4.803 × 10⁹⁵(96-digit number)
48037072498965571285…27303746987526918721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.607 × 10⁹⁵(96-digit number)
96074144997931142570…54607493975053837441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.921 × 10⁹⁶(97-digit number)
19214828999586228514…09214987950107674881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.842 × 10⁹⁶(97-digit number)
38429657999172457028…18429975900215349761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.685 × 10⁹⁶(97-digit number)
76859315998344914056…36859951800430699521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.537 × 10⁹⁷(98-digit number)
15371863199668982811…73719903600861399041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.074 × 10⁹⁷(98-digit number)
30743726399337965622…47439807201722798081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.148 × 10⁹⁷(98-digit number)
61487452798675931244…94879614403445596161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.229 × 10⁹⁸(99-digit number)
12297490559735186248…89759228806891192321
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,561,781 XPM·at block #6,789,726 · updates every 60s